The generator matrix

 1  0  0  0  1  1  1  2 2X+2  2  1  1  1  1 3X  1  1 3X  1  1  X  2  1  1  1  1  1  1  1 2X+2  1  X  1
 0  1  0  0 2X  1 2X+1  1  1  1 3X 2X+1  X 3X+1 X+2 X+3 3X+3  1 3X+1  2  0 2X  2 2X+3 X+2  X  3 2X+2 2X+1 2X+2 X+1  1 X+1
 0  0  1  0 2X+1  1 2X 2X+1 2X 3X+1  1 3X+2 X+2 3X+1  1 2X+3 X+3  X 2X+2  X  1  1 X+3 2X+2 3X+1 2X+1 3X+1  0 3X+3 3X+2 2X 2X+3 3X+2
 0  0  0  1  1 2X 2X+1 2X+1 2X+3  X  X 3X+2 X+1 X+3 2X+3  2  3 X+1  1 2X+2 2X+2 X+3 3X+1 X+2  2 2X+2 3X+1 X+3  0  1  X  3  1

generates a code of length 33 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+586x^28+2236x^29+4589x^30+7534x^31+11449x^32+12600x^33+11671x^34+7908x^35+4282x^36+1844x^37+643x^38+126x^39+46x^40+8x^41+9x^42+4x^44

The gray image is a code over GF(2) with n=264, k=16 and d=112.
This code was found by Heurico 1.16 in 16 seconds.